This argument assumes that the function f(x,y)=x^y is continuous near 0 and therefore lim (f(x)^g(x)) = (lim f(x))^(lim g(x)) at zero. But since it's not contin

This argument assumes that the function f(x,y)=x^y is continuous near 0 and therefore lim (f(x)^g(x)) = (lim f(x))^(lim g(x)) at zero. But since it's not continous, that formula does not necessarily hold true.